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We report a combined nano-photocurrent and infrared nanoscopy study of twisted bilayer graphene (TBG) enabling access to the local electronic phenomena at length scales as short as 20 nm. We show that the photocurrent changes sign at carrier densities tracking the local superlattice density of states of TBG. We use this property to identify domains of varying local twist angle by local photo-thermoelectric effect. Consistent with the photocurrent study, infrared nano-imaging experiments reveal optical conductivity features dominated by twist-angle dependent interband transitions. Our results provide a fast and robust method for mapping the electronic structure of TBG and suggest that similar methods can be broadly applied to probe electronic inhomogeneities of moir\'e superlattices in other van der Waals heterostructures.

Tungsten ditelluride (WTe2) is an atomically layered transition metal dichalcogenide whose physical properties change systematically from monolayer to bilayer and few-layer versions. In this report, we use apertureless scattering-type near-field optical microscopy operating at Terahertz (THz) frequencies and cryogenic temperatures to study the distinct THz range electromagnetic responses of mono-, bi- and trilayer WTe2 in the same multi-terraced micro-crystal. THz nano-images of monolayer terraces uncovered weakly insulating behavior that is consistent with transport measurements. The near-field signal on bilayer regions shows moderate metallicity with negligible temperature dependence. Subdiffractional THz imaging data together with theoretical calculations involving thermally activated carriers favor the semimetal scenario with $$\Delta \approx -10\,{{{\rm{meV}}}}$$ Δ ≈ − 10 meV over the semiconductor scenario for bilayer WTe2. Also, we observed clear metallic behavior of the near-field signal on trilayer regions. Our data are consistent with the existence of surface plasmon polaritons in the THz range confined to trilayer terraces in our specimens. Finally, data for microcrystals up to 12 layers thick reveal how the response of a few-layer WTe2 asymptotically approaches the bulk limit.

Tungsten ditelluride (WTe_2) is a transition metal dichalcogenide whose physical properties depend critically on the number of layers. In this paper, we use apertureless scattering-type near-field optical microscopy operating at Terahertz (THz) frequencies and cryogenic temperatures to identify distinct THz range electromagnetic behavior of WTe_2 mono-, bi- and tri-layer terraces in the same micro-crystals. We observed clear metallic behavior of the near-field signal on tri-layer regions. Our data are consistent with the existence of surface plasmon polaritons (SPP) in the THz range confined to tri-layer terraces in our specimens. The near-field signal on bi-layer regions surprisingly shows moderately metallicity, but with negligible temperature dependence. Subdiffractional THz imaging data together with theoretical calculations considering thermally activated carriers favor the semimetal scenario over the semiconductor scenario for bi-layer WTe_2. THz images for monolayer terraces uncovered weakly insulating behavior consistent with transport data.

Tungsten ditelluride (WTe2) is an atomically layered transition metal dichalcogenide whose physical properties change systematically from monolayer to bilayer and few-layer versions. In this report, we use apertureless scattering-type near-field optical microscopy operating at Terahertz (THz) frequencies and cryogenic temperatures to study the distinct THz range electromagnetic responses of mono-, bi- and trilayer WTe2 in the same multi-terraced micro-crystal. THz nano-images of monolayer terraces uncovered weakly insulating behavior that is consistent with transport measurements. The near-field signal on bilayer regions shows moderate metallicity with negligible temperature dependence. Subdiffractional THz imaging data together with theoretical calculations involving thermally activated carriers favor the semimetal scenario with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \approx -10\,{{{\rm{meV}}}}$$\end{document}Δ≈−10meV over the semiconductor scenario for bilayer WTe2. Also, we observed clear metallic behavior of the near-field signal on trilayer regions. Our data are consistent with the existence of surface plasmon polaritons in the THz range confined to trilayer terraces in our specimens. Finally, data for microcrystals up to 12 layers thick reveal how the response of a few-layer WTe2 asymptotically approaches the bulk limit., The behaviour of Tungsten ditelluride (WTe2) in few-layer form is not yet fully characterized. Here the authors use a near-field terahertz microscopy technique to observe the electromagnetic responses of WTe2 flakes from one to several layers and to study their semimetallic/ semiconducting behavior.

Plasmon polaritons are hybrid excitations of light and mobile electrons that can confine the energy of long-wavelength radiation at the nanoscale. Plasmon polaritons may enable many enigmatic quantum effects, including lasing 1 , topological protection2,3 and dipole-forbidden absorption 4 . A necessary condition for realizing such phenomena is a long plasmonic lifetime, which is notoriously difficult to achieve for highly confined modes 5 . Plasmon polaritons in graphene—hybrids of Dirac quasiparticles and infrared photons—provide a platform for exploring light–matter interaction at the nanoscale6,7. However, plasmonic dissipation in graphene is substantial 8 and its fundamental limits remain undetermined. Here we use nanometre-scale infrared imaging to investigate propagating plasmon polaritons in high-mobility encapsulated graphene at cryogenic temperatures. In this regime, the propagation of plasmon polaritons is primarily restricted by the dielectric losses of the encapsulated layers, with a minor contribution from electron–phonon interactions. At liquid-nitrogen temperatures, the intrinsic plasmonic propagation length can exceed 10 micrometres, or 50 plasmonic wavelengths, thus setting a record for highly confined and tunable polariton modes. Our nanoscale imaging results reveal the physics of plasmonic dissipation and will be instrumental in mitigating such losses in heterostructure engineering applications. The fundamental limits to plasmon damping in graphene are determined using nanoscale infrared imaging at cryogenic temperatures, and plasmon polaritons are observed to propagate over 10 micrometres in high-mobility encapsulated graphene.

We review recent discoveries of the intriguing plasmonic phenomena at a variety of electronic boundaries (EBs) in graphene including a line of charges in graphene induced by a carbon nanotube gate, grain boundaries in chemical vapor deposited graphene films, an interface between graphene and moire patterned graphene, an interface between graphene and bilayer graphene, and others. All these and other EBs cause plasmonic impedance mismatch at the two sides of the boundaries. Manifestations of this effect include plasmonic fringes that stem from plasmon reflections and interference. Quantitative analysis and modeling of these plasmonic fringes uncovered intriguing properties and underlying physics of the EBs. Potential plasmonic applications associated with these EBs are also briefly discussed.

Properties of atomic van der Waals heterostructures are profoundly influenced by interlayer coupling, which critically depends on stacking of the proximal layers. Rotational misalignment or lattice mismatch of the layers gives rise to a periodic modulation of the stacking, the moiré superlattice. Provided the superlattice period extends over many unit cells, the coupled layers undergo lattice relaxation, leading to the concentration of strain at line defects – solitons - separating large area commensurate domains. We visualize such long-range periodic superstructures in thin crystals of hexagonal boron nitride using atomic-force microscopy and nano-infrared spectroscopy. The solitons form sub-surface hexagonal networks with periods of a few hundred nanometers. We analyze the topography and infrared contrast of these networks to obtain spatial distribution of local strain and its effect on the infrared-active phonons of hBN., Solitons may develop when strain forms at line defects separating commensurate domains in misaligned or lattice-mismatched van der Waals heterostructures. Here, the authors use atomic-force microscopy and nano-infrared spectroscopy to image solitons in thin hBN crystals in the form of long-range periodic superstructures, creating sub-surface hexagonal networks with periods of a few hundred nanometers.

Phonon polaritons in van der Waals materials reveal significant confinement accompanied with long propagation length: important virtues for tasks pertaining to the control of light and energy flow at the nanoscale. While previous studies of phonon polaritons have relied on relatively thick samples, here reported is the first observation of surface phonon polaritons in single atomic layers and bilayers of hexagonal boron nitride (hBN). Using antenna-based near-field microscopy, propagating surface phonon polaritons in mono- and bilayer hBN microcrystals are imaged. Phonon polaritons in monolayer hBN are confined in a volume about one million times smaller than the free-space photons. Both the polariton dispersion and their wavelength-thickness scaling law are altered compared to those of hBN bulk counterparts. These changes are attributed to phonon hardening in monolayer-thick crystals. The data reported here have bearing on applications of polaritons in metasurfaces and ultrathin optical elements.

We present a comprehensive study of the reflection of normally incident plasmon waves from a low-conductivity 1D junction in a 2D conductive sheet. Rigorous analytical results are derived in the limits of wide and narrow junctions. Two types of phenomena determine the reflectance, the cavity resonances within the junction and the capacitive coupling between the leads. The resonances give rise to alternating strong and weak reflection but are vulnerable to plasmonic damping. The capacitive coupling, which is immune to damping, induces a near perfect plasmon reflection in junctions narrower than $1/10$ of the plasmon wavelength. Our results are important for infrared 2D plasmonic circuits utilizing slot antennas, split gates or nanowire gates. They are also relevant for the implementation of nanoscale terahertz detectors, where optimal light absorption coincides with the maximal junction reflectance.

Twisting a route for surface plasmons Graphene is an atomically thin material that supports highly confined plasmon polaritons, or nano-light, with very low loss. The properties of graphene can be made richer by introducing and then rotating a second layer so that there is a slight angle between the atomic registry. Sunku et al. show that the moiré patterns that result from such twisted bilayer graphene also provide confined conducting channels that can be used for the directed propagation of surface plasmons. Controlling the structure thereby provides a pathway to control and route surface plasmons for a nanophotonic platform. Science , this issue p. 1153

Domain walls separating regions of AB and BA interlayer stacking in bilayer graphene have attracted attention as novel examples of structural solitons, topological electronic boundaries, and nanoscale plasmonic scatterers. We show that strong coupling of domain walls to surface plasmons observed in infrared nanoimaging experiments is due to topological chiral modes confined to the walls. The optical transitions among these chiral modes and the band continua enhance the local ac conductivity, which leads to plasmon reflection by the domain walls. The imaging reveals two kinds of plasmonic standing-wave interference patterns, which we attribute to shear and tensile domain walls. We compute the electronic structure of both wall varieties and show that the tensile wall contain additional confined bands which produce a structure-specific contrast of the local conductivity. The calculated plasmonic interference profiles are in quantitative agreement with our experiments., Comment: 14 pages, 5 figures

We show that surface plasmons of a two-dimensional Dirac metal such as graphene can be reflected by line-like perturbations hosting one-dimensional electron states. The reflection originates from a strong enhancement of the local optical conductivity caused by optical transitions involving these bound states. We propose that the bound states can be systematically created, controlled, and liquidated by an ultranarrow electrostatic gate. Using infrared nanoimaging, we obtain experimental evidence for the locally enhanced conductivity of graphene induced by a carbon nanotube gate, which supports this theoretical concept., Comment: 14 pages, 12 figures, submitted to PRL

The problem of electrostatic screening of a charged line by undoped or weakly doped graphene is treated beyond the linear-response theory. The induced electron density is found to be approximately doping independent, n(x)~(log x)^2/x^2, at intermediate distances x from the charged line. At larger x, twin p-n junctions may form if the external perturbation is repulsive for graphene charge carriers. The effect of such inhomogeneities on conductance and quantum capacitance of graphene is calculated. The results are relevant for transport properties of graphene grain boundaries and for local electrostatic control of graphene with ultrathin gates., Comment: Fixed typos and added references

Electromagnetic interaction between a sub-wavelength particle (the `probe') and a material surface (the `sample') is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton modes localized near the probe. The resonance parameters depend on the dielectric function and geometry of the probe, as well as the surface reflectivity of the material. Calculation of such resonances is carried out for several types of axisymmetric probes: spherical, spheroidal, and pear-shaped. For spheroids an efficient numerical method is developed, capable of handling cases of large or strongly momentum-dependent surface reflectivity. Application of the method to highly resonant materials such as aluminum oxide (by itself or covered with graphene) reveals a rich structure of multi-peak spectra and nonmonotonic approach curves, i.e., the probe-sample distance dependence. These features also strongly depend on the probe shape and optical constants of the model. For less resonant materials such as silicon oxide, the dependence is weak, so that the spheroidal model is reliable. The calculations are done within the quasistatic approximation with the radiative damping included perturbatively., Comment: 25 pages, 15 figures. Minor changes to improve presentation

Conventional second-harmonic-generation anisotropy of collagen is modeled with cylindrical symmetry. We demonstrated that with thin fibrils, trigonal symmetry of constituent triple-helix molecules dominates the anisotropy, but it converged into cylindrical symmetry with thicker fibrils.